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Results tagged with mg.metric-geometry
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user 1306
Euclidean, hyperbolic, discrete, convex, coarse geometry, metric spaces, comparisons in Riemannian geometry, symmetric spaces.
5
votes
About a solid which satisfies $\sum_{i=1}^{n}x_i=0, |x_i|\le1\ (i=1,2,\cdots,n)$
Section 2 in the paper http://arxiv.org/abs/math/0503115 expresses this volume in terms of sinc integrals $$\sigma_n=\frac2\pi\int_0^\infty \left(\frac{\sin x}{x}\right)^n\,dx$$
Namely, it is shown th …
- 16.9k
14
votes
Packing obtuse vectors in $\mathbb{R}^d$
I always give this as an exercise in my linear algebra class in the form:
If $k+1$ vectors in $\mathbb{R}^n$ form obtuse angles with one another, then after removing any one vector from that collecti …
- 16.9k